Question

Which of the following is a correct statement? Which of the following is the right choice? Explain your answer.

(A) The probability of a Type II error does not depend on the probability of a Type I error.

(B) In conducting a hypothesis test, it is possible to simultaneously make both a Type I and a Type II error.

(C) A Type II error will result if one incorrectly assumes the data are normally distributed.

(D) When you choose a significance level a, you're setting the probability of a Type I error to exactly a.

Answer 1

(D) When you choose a significance level a, you're setting the probability of a Type I error to exactly a.

This statement is correct. In hypothesis testing, the significance level (\(\alpha\)) represents the probability of making a Type I error, which occurs when you reject a null hypothesis that is actually true. By setting the significance level, you determine the threshold for how extreme the observed data must be in order to reject the null hypothesis. The probability of a Type I error is equal to the chosen significance level (\(\alpha\)). For example, if you choose a significance level of 0.05, you're accepting a 5% chance of making a Type I error.